Provided .
x- 1= 1- x reduces to 2x= 2 and then x= 1. Yes, that is satisifies x- 1= 0 and so is a valid solution.

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Provided x- 1< 0.
1-x= 1- x reduces to 0= 0 which is true for all x but we still have "x- 1< 0". Every x such that x- 1< 0, which says x< 1, is a solution. Putting that together with the first case says that all x such that is a solution.

and the answer is supposed to be the inequality but ive no clue how to get to this.